Precision two-way time transfer over meteorburst communications channels

ABSTRACT

Systems and methods for clock synchronization are disclosed. A client synchronization system (CSS) may transmit RF pulses to a server CSS over micrometeorite ionization trail (MMIT) channels, and may receive RF pulses from the server CSS over MMIT channels, each received RF pulse following transmitted RF pulse. The client CSS may receive from the server CSS over MMIT channels measurement data including pulse arrival times at the server CSS. The measurement and transmission data may be correlated to identify RF-pulse pairs, each pairing a transmitted RF pulse received by the server CSS with a received RF pulse received from the server CSS, both over the same MMIT. TWTT analysis may be applied to timing data the pairs to compute time offsets between a client clock and a server clock. An analytical model of clock drift may be applied to the offsets to synchronize the client clock to the server clock.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. provisional patent applicationNo. 63/219,062, filed Jul. 7, 2021, which is hereby incorporated byreference in its entirety.

GOVERNMENT RIGHTS

This invention was made with Government support under contractFA8650-13-C-7331 awarded by the Air Force Research Laboratory and undercontract FA2487-18-D-0001, Delivery Order FA2487-19-F-1073 awarded bythe United States Air Force. The Government has certain rights in theinvention.

BACKGROUND

Micrometeorite ionization trails (MMITs) are created by billions of tinymeteorites entering Earth's atmosphere. The kinetic energy of theseparticles is high enough to ionize in the atmosphere immediately alongthe micrometeorite paths between 80 and 100 km altitude, generating longtrails of electrons and ions. The electrons remain free and diffuse forup to hundreds of milliseconds before recombining with nitrogen.Radio-frequency radiation between 30-80 MHz impinging on the freeelectrons causes the electrons to oscillate and re-radiate energy in adipole pattern via Thompson scattering. If RF radiation is transmittedupwards from the ground, a portion of the RF radiation may be scatteredback down to the ground at a different location. MMITs can thuseffectively act as RF channels, which may be used for radiocommunications between widely separated ground stations.

More particularly, the MMITs are known to occur randomly in time andlocation in an approximate altitude range of 80-100 km of the Earth'satmosphere, have lifetimes of random duration, and randomly-distributedtrail lengths. These characteristics have been well-studied so it ispossible to determine the statistical properties of MMIT channels intime and space. As such, an expected effectiveness RF communications viaMMIT channels for various applications may be reasonably predicted. MMITevents are also sometimes referred to as “meteor bursts” and RFcommunications via MMIT channels is also sometimes referred to as“meteor burst communications.”

SUMMARY

Clocks may be synchronized using various techniques. For high accuracy,global synchronization, a conventional approach may involve using theGlobal Positioning System (GPS) or other Global Navigation SatelliteSystems (GNSS). However, this approach depends on an external systemthat can have limited availability in certain circumstances (e.g., dueto radio interference, GPS system readiness, etc.). Alternativeapproaches can involve establishing a two-way communications linkbetween two sites where clocks can be synchronized and then calibratedfor the channel latency. However, such approaches require deployment ofexpensive, dedicated infrastructure (e.g., a terrestrial microwave link,and an optical fiber link, or a service lease on a satellitetransponder). For example, the U.S. Naval Observatory provides a two-waytime transfer service based on the use of satellite relays. This serviceuses specialized equipment to control highly accurate clocks (e.g.,hydrogen masers) using satellite terminals, so it has a highinstallation cost and a high monthly service cost.

The above two examples of conventional approaches to global clocksynchronization share drawbacks that make them unsuitable and/orimpractical for a wide variety of clock synchronization applicationsthat need or require low-cost, portable, and/or field-deployablesolutions. The inventors have recognized that the drawbacks ofconventional approaches are due, at least in part, to the cost andcomplexity of specialized equipment, and to reliance on thecommunications infrastructure of inter-site communications. Theinventors have further recognized that the impediments to devising anddeploying low-cost synchronization systems that are independent ofinfrastructure can be overcome by utilizing MMIT channels forcommunicating both two-way timing signals, as well as measurement databetween pairs of ground stations. In particular, the inventors havesignificantly extended previous MMIT-based two-way time transfer (TWTT)demonstration techniques to design and develop systems and methods forcontinuous, highly accurate and precise distributed clocksynchronization that can operate using only MMIT channels.

Accordingly, in one aspect, example embodiments may involve a clientclock synchronization system (CSS) configured for communications with aserver CSS over micrometeorite ionization trail (MMIT) channels. MMITchannels are known to be distributed randomly in both time and locationwithin the Earth's ionosphere, and have lifetimes distributed randomlyin duration. The client CSS may include: an antenna; a transceivercoupled with the antenna and configured for switching between transmitand receive modes; and a computing system coupled with the transceiverand with a client clock. The computing system may be configured forcarrying out operations including: via the antenna, with the transceiverin transmit mode, transmitting a sequence of radio-frequency (RF) pulsesto the server CSS over a first multiplicity of MMIT channels, whereintransmission information indicating a respective local transmitidentifier and respective transmission time of each transmitted RF pulseis maintained at the client CSS; via the antenna, with the transceiverin receive mode, receiving a first plurality of RF pulses from theserver CSS over a second multiplicity of MMIT channels, each received RFpulse consecutively following one of the transmitted RF pulses of thesequence, wherein reception information indicating a respective localreceive identifier and arrival time of each received RF pulse ismaintained at the client CSS; via the antenna, with the transceiver inreceive mode, receiving measurement data from the server CSS over athird multiplicity of MMIT channels, wherein the measurement datacomprise, for each of a second plurality of RF pulses received by theserver CSS, a respective remote receive identifier, a respective arrivaltime at the server CSS, and a respective signal-to-noise (SNR)measurement; correlating the measurement data with the transmissioninformation to identify respective transmitted RF pulses of the sequencewith respective RF pulses of the second plurality received by the serverCSS at the respective arrival times with the respective SNRmeasurements; correlating the transmission times of the identifiedrespective transmitted RF pulses with the reception information todetermine a third plurality of respective RF-pulse pairs, wherein eachrespective RF-pulse pair comprises (i) a particular transmitted RF pulsethat was received by the server CSS over a particular MMIT channel and(ii) a particular RF pulse that was received from the server CSS overthe same particular MMIT channel and consecutively followingtransmission of the particular transmitted RF pulse; applying two-waytime transfer (TWTT) analysis to timing data of each RF-pulse pair tocompute a set of time offsets of the client clock with respect to aserver clock of the server CSS; and applying an analytical model ofclock drift to the set of time offsets to synchronize the client clockwith the server clock.

In another aspect, example embodiments may involve a server clocksynchronization system (CSS) configured for communications with a clientCSS over micrometeorite ionization trail (MMIT) channels. MMIT channelsare known to be distributed randomly in both time and location withinthe Earth's ionosphere and have lifetimes distributed randomly induration. The server CSS may include: an antenna; a transceiver coupledwith the antenna and configured for switching between transmit andreceive modes; and a computing system coupled with the transceiver andwith a server clock. The computing system may be configured for carryingout operations including: a computing system coupled with thetransceiver and with a client clock, and configured for carrying outoperations including: via the antenna, with the transceiver in transmitmode, transmitting a sequence of radio-frequency (RF) pulses to theclient CSS over a first multiplicity of MMIT channels; via the antenna,with the transceiver in receive mode, receiving a first plurality of RFpulses from the client CSS over a second multiplicity of MMIT channels,each consecutively following one of the transmitted RF pulses of thesequence, wherein reception information indicating a respective localreceive identifier and arrival time of each received RF pulse ismaintained at the client CSS; via the antenna, with the transceiver inreceive mode, transmitting measurement data to the client CSS over athird multiplicity of MMIT channels, wherein the measurement datacomprise, for each of a sub-plurality of the first plurality of RFpulses received by the server CSS, a respective local receiveidentifier, the respective arrival time at the server CSS, and arespective signal-to-noise (SNR) measurement.

In yet another aspect, example embodiments may involve a method of clocksynchronization carried out by a client synchronization system (CSS)configured for communications with a server CSS over micrometeoriteionization trail (MMIT) channels. MMIT channels are known to bedistributed randomly in both time and location within the Earth'sionosphere, and have lifetimes distributed randomly in duration. Themethod may involve operations including: via an antenna, with atransceiver in transmit mode, transmitting a sequence of radio-frequency(RF) pulses to a server CSS over a first multiplicity of MMIT channels,wherein transmission information indicating a respective local transmitidentifier and respective transmission time of each transmitted RF pulseis maintained at the client CSS; via the antenna, with the transceiverin receive mode, receiving a first plurality of RF pulses from theserver CSS over a second multiplicity of MMIT channels, each received RFpulse consecutively following one of the transmitted RF pulses of thesequence, wherein reception information indicating a respective localreceive identifier and arrival time of each received RF pulse ismaintained at the client CSS; via the antenna, with the transceiver inreceive mode, receiving measurement data from the server CSS over athird multiplicity of MMIT channels, wherein the measurement datacomprise, for each of a second plurality of RF pulses received by theserver CSS, a respective remote receive identifier, a respective arrivaltime at the server CSS, and a respective signal-to-noise (SNR)measurement; correlating the measurement data with the transmissioninformation to identify respective transmitted RF pulses of the sequencewith respective RF pulses of the second plurality received by the serverCSS at the respective arrival times with the respective SNRmeasurements; correlating the transmission times of the identifiedrespective transmitted RF pulses with the reception information todetermine a third plurality of respective RF-pulse pairs, wherein eachrespective RF-pulse pair comprises (i) a particular transmitted RF pulsethat was received by the server CSS over a particular MMIT channel and(ii) a particular RF pulse that was received from the server CSS overthe same particular MMIT channel and consecutively followingtransmission of the particular transmitted RF pulse; applying two-waytime transfer (TWTT) analysis to timing data of each RF-pulse pair tocompute a set of time offsets of the client clock with respect to aserver clock of the server CSS; and applying an analytical model ofclock drift to the set of time offsets to synchronize a client clock ofthe client CSS with a server clock of the server CSS.

In still another aspect, example embodiments may involve an article ofmanufacture including a non-transitory computer-readable medium, havingstored thereon program instructions that, when executed by one moreprocessors of a system, cause the system to carry out various operationsof the example methods and/or steps of the above embodiments.

These, as well as other embodiments, aspects, advantages, andalternatives, will become apparent to those of ordinary skill in the artby reading the following detailed description, with reference whereappropriate to the accompanying drawings. Further, this summary andother descriptions and figures provided herein are intended toillustrate embodiments by way of example only and, as such, thatnumerous variations are possible. For instance, structural elements andprocess steps can be rearranged, combined, distributed, eliminated, orotherwise changed, while remaining within the scope of the embodimentsas claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified block diagram showing components of a clocksynchronization system, in accordance with example embodiments.

FIG. 2 illustrates a schematic drawing of a computing device, accordingto an example embodiment.

FIG. 3 illustrates a schematic drawing of a networked server cluster,according to an example embodiment.

FIG. 4 illustrates timing and delay characteristics of an exampleoperational scenario of a clock synchronization system, in accordancewith example embodiments.

FIG. 5A illustrates example transmit and receive modes of example pulserepetition intervals of an example clock synchronization system, inaccordance with example embodiments.

FIG. 5B is a conceptual illustration of example transmissions andreceptions between server and client stations of an example clocksynchronization system over micrometeorite ionization trail channels, inaccordance with example embodiments.

FIG. 6 illustrates example timing processing and clock correctionscarried out by a client station of an example clock synchronizationsystem, in accordance with example embodiments.

FIG. 7 illustrates an example RF pulse in frequency space, in accordancewith example embodiments.

FIG. 8 illustrates an example RF pulse detection and arrival timemeasurement, in accordance with example embodiments.

FIG. 9 is a flow chart of an example method, in accordance with exampleembodiments.

DETAILED DESCRIPTION

Example methods, devices, and systems are described herein. It should beunderstood that the words “example” and “exemplary” are used herein tomean “serving as an example, instance, or illustration.” Any embodimentor feature described herein as being an “example” or “exemplary” is notnecessarily to be construed as preferred or advantageous over otherembodiments or features unless stated as such. Thus, other embodimentscan be utilized and other changes can be made without departing from thescope of the subject matter presented herein.

Accordingly, the example embodiments described herein are not meant tobe limiting. It will be readily understood that the aspects of thepresent disclosure, as generally described herein, and illustrated inthe figures, can be arranged, substituted, combined, separated, anddesigned in a wide variety of different configurations.

Further, unless context suggests otherwise, the features illustrated ineach of the figures may be used in combination with one another. Thus,the figures should be generally viewed as component aspects of one ormore overall embodiments, with the understanding that not allillustrated features are necessary for each embodiment.

Additionally, any enumeration of elements, blocks, or steps in thisspecification or the claims is for purposes of clarity. Thus, suchenumeration should not be interpreted to require or imply that theseelements, blocks, or steps adhere to a particular arrangement or arecarried out in a particular order.

I. Example Meteroburst-Based Two-Way Time Transfer Clock SynchronizationSystem

For two hypothetically, perfectly synchronized clocks, both would haveidentical phases (e.g., time settings) and identical frequencies. Inpractice, imperfect synchronization may lead to a time offset betweentwo clocks that will grow with time if the frequencies are also notperfectly identical. Non-identical frequencies may also be referred toas relative frequency drift, and may result in time drift between twoclocks. Synchronization of two clocks generally considers one of theclocks to be a reference, and aims to align the phase and frequency ofthe other clock with the reference. A single reference clock may also beused to synchronize multiple other clocks. Note that the term “phase”used in comparing two clocks may be considered as analytically relatedto time instants as measured by the clocks.

In applications requiring nanosecond-level synchronization, frequencydifferences between oscillators can be a significant factor. Forexample, a frequency drift of just one part in 10¹² can result in a timeoffset of 100s of nanoseconds (one nanosecond=10⁻⁹ seconds) per hour. Tomaintain time synchronization to within a few nanoseconds, then, evenhigh-precision oscillators, such as rubidium standards, can introduceunacceptable errors if left uncorrected even over relatively short timeintervals. This is just one illustration of the need for synchronizationto account for both time and frequency drift in high accuracy andprecision applications.

Example embodiments are describe herein of systems and methods forsynchronization between a server clock and one or more client clocks byway of exchange of timing signals and measurement data transmitted atradio frequencies over radio-frequency (RF) channels created bymicrometeorite ionization trails (MMITs) in the Earth's atmosphere. Moreparticularly, example systems and methods use two-way time transfer(TWTT) techniques over MMIT channels to achieve clock synchronization.The server clock may be a reference clock and be part of a serverstation, and the client clocks may be part of respective clientstations. For purposes of discussion herein, only one client clock andclient station will be considered. However, the principles and operationdescribed may be straightforwardly extended to multiple client clocksand client stations. In an example scenario, the server and clientstation may both be ground stations that are widely separatedgeographically. A non-limiting example ground distance between a serverand client stations is 300-500 km, though other distances are possible.An approximate maximum range may be determined from a simplifiedgeometry of two separated ground stations and a reflection point betweenthem at an altitude typical of MMITs.

As described in detail below, TWTT over MMIT channels entails exchangebetween a server and a client station of pairs of timing signals overthe same MMIT channel. From various studies, it is known that MMITs arerandom, transient events, and thus, so are potential RF channels thatthey create. As such, opportunities for the two stations to exchangeparticular RF signals on the same MMIT channel are similarly random,transient opportunities. Based on statistical distributions of MMIToccurrences, properties, and characteristics, and accounting for certainaspects of operating principles of the system, as described below, itmay be predicted that there can be roughly 20-50 MMIT channels per houruseable for the exchange of timing signals. From among theseopportunities, measurement data from only a subset of successfullyexchanged timing signals may ultimately be selected and applied in TWTTanalysis, for reasons explained below.

In accordance with example embodiments, the measurement data from thesubset of exchanged timing signals used in the TWTT analysis mayintermittently yield a derived time offset (or “time delta”) estimatebetween the server and client clocks. Due to the temporally randomnature of MMIT channels, as well as selection of the subset ofmeasurement data of exchanged timing signals, the derived time offsetestimates may tend to be sparsely and irregularly distributed in time,and may be thought of as a sort of stream of intermittent the“time-delta measurements.” In further accordance with exampleembodiments, additional analytical techniques may be applied to thetime-delta measurements to drive a control model/algorithm that maycontinuously (or nearly so) update the client clock to maintainsynchronization with the server clock. In particular, analyticaltechniques have been devised that account for the sparse and irregularcharacter of the time delta measurements.

In a further aspect of example embodiments, arrival time measurements oftiming signals received at the server station that form the measurementdata used in the TWTT analysis may be transmitted to the client stationalso over MMIT channels. Doing so enables the overall system to beentirely independent of any communications infrastructure and/orexpensive time-distribution technologies. Advantageously, this allows asystem made up of a server station and client station to be lessexpensive than one that relies on such infrastructure and/ortechnologies, as well as be field-deployable. Other benefits accrue fromthe essentially standalone implementation as well. It should beunderstood that other embodiments could nevertheless connect orintegrate with communications infrastructure and/or time-distributionsystems, at least for purposes of testing and/or calibration, forexample. The basic principles of TWTT over MMIT channels that could beused in such alternative embodiments remain the same.

An example system architecture is described below, followed by a moregeneral description of example computing systems and devices, andexample configurations of computing systems and devices. Subsequentsections describe example operation and methods.

A. Example System Architecture

FIG. 1 is a simplified block diagram showing components of an exampletwo-way time transfer (TWTT) clock synchronization system 100 configuredfor communication of timing signals and data over radio-frequency (RF)channels created by micrometeorite ionization trails (MMITs) in theEarth's atmosphere, in accordance with example embodiments. The blockdiagram of FIG. 1 may also be considered as depicting aspects of anoperational architecture of the TWTT clock synchronization system 100.Some of the components of the TWTT clock synchronization system 100 maybe structural, such as amplifiers and filters, and others may beidentified in terms of their operation or function. Operational and/orfunctional components could be implemented as software and/or hardwareand/or firmware, for example, and may sometimes be referred to herein as“modules” for the purpose of the present discussion.

The TWTT clock synchronization system 100 can also include one or moreconnection mechanisms that connect various components within the system100. By way of example, the connection mechanisms are depicted as arrowsbetween components. The direction of an arrow may indicate a directionof information flow, though this interpretation should not be viewed aslimiting. In this disclosure, the term “connection mechanism” means amechanism that connects and facilitates communication between two ormore components, devices, systems, or other entities. A connectionmechanism can include a relatively simple mechanism, such as a cable orsystem bus, and/or a relatively complex mechanism, such as apacket-based communication connection. In some instances, a connectionmechanism can include a non-tangible medium, such as in the case wherethe connection is at least partially wireless. A connection mechanismmay also include programmed communication between software and/orhardware modules or applications, such as application program interfaces(APIs), for example.

While an aspect of the example embodiments may be to avoid dependence oncommunications infrastructure, the TWTT clock synchronization system 100may still include capabilities for such communications, at least fortesting and/or development purposes, for example. Thus, in thisdisclosure, in addition to direct connections between components, aconnection may in some instances also be indirect, passing throughand/or traversing one or more entities, such as a router, switcher, orother network device. Likewise, in this disclosure, communication (e.g.,a transmission or receipt of data), while generally direct, may in somecircumstances be indirect.

As shown, the example TWTT clock synchronization system 100 includes aserver station 100-S, depicted on the left side of FIG. 1 , and a clientstation 100-C, depicted on the right side. The client station 100-C maybe an example of what may more generally be referred to as a “clientclock synchronization system” or “client CSS.” Likewise, the serverstation 100-S may be an example of what may more generally be referredto as a “server clock synchronization system” or “server CSS.”

In addition to the two stations, FIG. 1 also includes a conceptualillustration of an MMIT channel, depicted as a sloping dashed line atthe top of the figure, and labeled “micrometeorite ionization trail.”Bi-directional zig-zag arrows between antennas 106 of the stations andthe MMIT channel represent RF signals transmitted in both directionsbetween the two stations over a single MMIT channel. As mentioned above,MMITs—and thus potential RF channels that they create—are random,transient events. As such, opportunities for the two stations toexchange particular RF signals on the same MMIT channel are similarlyrandom, transient opportunities. Some of the operations described beloware carried out regardless of whether any MMIT channel happens to beavailable, and others are carried out specific to one or moredeterminations that an MMIT channel has been successfully utilized forRF signal transmission from one or both stations to the other.

Both stations 102-S and 102-C may be largely identical in terms of thecomponents shown in FIG. 1 , although, as described below, some aspectsof their respective operations may differ. Some common features andcomponents of the server station 100-S and the client station 100-Cinclude an antenna 106, a transmit/receive switch 110 (e.g.,transceiver), a power amplifier 108, a digital-to-analog converter (DAC)112, a software-defined radio 104 having a transmit waveform converter104-Tx and a receive waveform demodulator 104-Rx, an analog-to-digitalconverter (ADC) 114, a low-noise amplifier 120, a bandpass filter 118,and a limiter 116. Both stations also include a delay generator 134 anda clock, 136-S for the server station and 136-C for the client station.While the clock hardware may be identical for both stations, such as arubidium time/frequency standard, the two clocks are labeleddistinctively to indicate a general scenario of lack of synchronizationbetween them that system operations aim to correct.

In example embodiments, the client clock may include, or be integratedin, a device that enables the clock to be adjusted. In particular, clockadjustments may include setting the phase (i.e., current time) andfrequency of an oscillator used to drive the clock. The ability toadjust the clock in this manner may allow the clock to be “steered”according to correction measurements, as described in more detail below.In some example embodiments, server clock may also include the same orsimilar means for adjustment. It should be understood that there may bea variety of clock hardware/software/firmware implementations that maybe used in example embodiments. Non-limiting examples of such variationsinclude fully hardware implementations withhardware-controllable/adjustable oscillators, and softwareimplementations with programmable control/adjustment of timing signals.

Both stations further include respective computing systems, 102-S forthe server and 102-C for the client station. The computing systems 102-Sand 102-C may include, among other features and components described byway of example below in connection with FIG. 2 , a processor and memorystoring instructions that, when executed by the processor, cause thecomputing systems to carry out various operations and functionsdescribed herein. While the two computing systems 102-S and 102-C may belargely the same, each may implement particular operations and/orfunctions specific to their respective stations. Aside from a processorand memory, common aspects of both computing systems include a matchedfilter 122, a pulse detector 124, an arrival time analyzer 126, and adigital waveform generator 132. In addition, the server computing system102-S includes a measurement data selector 128 and a measurement dataformatter 130. Likewise, the client computing system 102-C furtherincludes a measurement data analyzer 140 and a clock errorcalculator/controller 138. The various components of the two computingsystems may themselves be implemented as hardware, software, and/orfirmware, for example.

The TWTT clock synchronization system 100 may include additionalcomponents besides those described above. Some embodiments may alsoinclude different components as well.

General operation of the server and client stations 100-S and 100-C maybe illustrated by way of example as follows. As described in detailbelow, each station may be configured to transmit RF pulse signals incontinuous (or nearly-continuous) regular, periodic pulse repetitionintervals (PRIs), each of which includes one transmit window followed byone receive window. During each transmit window each station may operatein transmit mode to transmit an RF pulse signal, and during each receivewindow each station may operate in a receive mode to listen for, and ifpresent (i.e., received) detect, a received RF pulse signal. As such,each station may be configured to operate in periodically alternatingtransmit and receive modes aligned with respective sequences of PRIs.The periodicity of the PRIs at each station may be controlled byperiodic timing pulses emitted by the respective clocks 136-S and 136-C.

In accordance with example embodiments, the delay generator 134 in eachstation may be configured to ensure that the transmit and receivewindows of each PRI are of specified durations and properly aligned withPRI boundaries. In addition, as also described in detail below, therelative timing of the PRIs at the server and client stations may bearranged such that the receive windows at each station are (at leastapproximately) aligned with time intervals during which pulsestransmitted from the other station would be expected to be received overavailable MMIT channels. Thus, in further accordance with exampleembodiments, the delay generator 134 in each station may also beconfigured to introduce an appropriate time offset between PRIs at thetwo stations so as to achieve interleaving of transmitted and (whenpresent) received RF pulse signals at each station. The time offsetbetween PRIs at the two stations may also be described as staggeredtransmit windows at the two stations. It should be noted that the timeoffset between PRIs at the two stations may be configured deliberatelyto achieve transmit and receive interleaving at each station, and shouldnot be confused with a time offset between the server clock 135-S andclient clock 136-C that represents a synchronization error that systemoperation aims to correct.

In the example illustrated in FIG. 1 , each delay generator 134periodically emits alternating Tx triggers and Rx gating windows to therespective computing system 102-S or 102-C to cause either the digitalwaveform generator 132 to generate pulse waveforms for transmission, orthe matched filter 122 to attempt detection of potentially-received RFpulses. Each delay generator 134 also periodically emits correspondingalternating Tx/Rx switch control signals to the respectivetransmit/receive switch 110 to cause it to switch between transmit andreceive modes of each PRI in coordination with transmit and receiveoperations of the respective computing system 102-S or 102-C. Note thatthe transmit/receive switch 110, in coordination with the poweramplifier 108, may be considered a transceiver.

In transmit mode, the transmit waveform converter 104-Tx of each stationgenerates a transmit waveform from the input of the respective digitalwaveform generator 132, and supplies the transmit waveform to therespective DAC 112. The resulting analog signal is amplified by therespective power amplifier 108 and input to the respectivetransmit/receive switch 110, which, in transmit mode, transmits theresulting RF pulse via the respective antenna 106. In an exampleembodiment, the amplifier 108 may be or include a 1.5 kW RF amplifier;that is, it may produce a 1.5 kW RF signal for transmission. Otheramplifier powers may be used as well.

While transmit mode operations may be configured to always result intransmission of an RF pulse (or, as described below, data transmissionin data communications mode), receive mode operations generally operatewhether or not an actual pulse is received at the respective antenna106. Any pulse (or data communication) received during receive mode andmatching the matched filter 122 will be detected, but not all receivemodes are necessarily temporally-coincident with a received pulse, andthus not all receive modes will yield a pulse detection (or datacommunication). But receive mode operations up through pulse detectionare generally the same, regardless of whether or not a pulse (or datacommunication) is actually detected.

In receive mode, the respective transmit/receive switch 110 passes itsoutput to the respective limiter 116, which may reduce the power of theinput signal as necessary before passing the input signal to therespective low-noise amplifier 120. The amplified signal of therespective low-noise amplifier 120 is input to the ADC 114, whichsupplies the digitized signal to the respective receive waveformdemodulator 104-Rx. More specifically, the output of the ADC 114 may bedigitized samples of the amplified signal produced at a particularsampling rate. In an example embodiment, a sampling rate of 25 MHz isused. Samples may be continually collected for the duration of receivemode operation. The respective matched filter 122 is next applied to theoutput, demodulated waveform, and the respective pulse detector 124evaluates the matched filter output to determine if a pulse has beendetected. This evaluation may involve a threshold test for detection,for example. It should be understood that other sampling rates could beused. A non-limiting example of a range of sampling rates is 10 MHz to100 MHz.

If a pulse is detected, it may be analyzed by the respective arrivaltime analyzer 126 to determine the pulse arrival time as measured withrespect to timekeeping of the respective clock 136-S or 136-C. Inaccordance with example embodiments, a form of interpolation may beapplied to the digitized samples to derive a time position of the peakof each detected pulse with a higher time resolution than the samplingrate. In addition, the arrival time may be measured with respect to thestart of a receive window aligned with the start having the switch inreceive mode, as describe below.

At this point, example operations of the server station 102-S and clientstation 102-C may differ in some aspects. More particularly, the serverstation 102-S may be configured to transmit certain measurement data,including pulse arrival times and identifications of the PRIs in whichthe pulses were received, to the client station 102-C, while operatingin a communications mode. Correspondingly, the client station 102-C maybe configured to receive the transmitted measurement data, also whileoperating in a communications mode, and the correlate PRIs of RF pulsesat the server station with PRIs of RF pulses transmitted to the serverstation. Such correlations may be used to identify RF pulse pairs thateach include one pulse transmitted by each station and received by theother over the same MMIT channel. The measured arrival times of the twopulses in each pair can be used in a TWTT analysis to determine a timeoffset error (or time delta) between the two clocks 136-S and 136-C at atime associated with the pulse transmissions. After determining the timeoffset error, the offset may be sequentially processed by the clientstation 100-C to synchronize its clock 136-C with the clock 136-S of theserver station 100-S.

In accordance with example embodiments, data transmission used fortransmitting measurement data from the server station 100-S to theclient station 100-C during the data communications mode may alsoutilize MMIT channels. As such, the volume of measurement data that canbe transmitted may be limited in part by the transient, randomavailability of MMIT channels. Thus, in typical operation, there may bemore arrival time measurement data collected by the server station 100-Sthan can be ultimately transmitted to the client station 100-C. Thiscircumstance may be addressed by judicious selection by the serverstation 100-S of which measurement data to transmit to the clientstation 100-C.

In further accordance with example embodiments, the measurement dataselector 128 may implement one or another form of selection algorithm tomake this data selection. The selected measurement data may then beformatted by the measurement data formatter 130 for transmission to theclient station 100-C using the data communications mode. The arrowsrepresenting the selected data input to the measurement data formatter,and the formatted data input to the digital waveform generator 132 aredepicted with dotted lines to signify data communications operations.

At the client station 100-C during data communications operations,received measurement data may be input to the measurement data analyzer140. As noted, measurement data from the server station 100-S mayinclude arrival times RF pulses, as well as associated PRI identifiersand signal-to-noise (SNR) measurements of the received pulses. Themeasurement data analyzer 140 may use the PRI identifiers to identifyeach pulse reported as received by the server station 100-S with itscorresponding RF transmission from the client station 100-C. Themeasurement data analyzer 140 may then input the results to the clockerror calculator/controller 138, which may attempt to pair eachtransmitted RF pulse known to be received by the server station 100-Swith an RF pulse received from the server station 100-S during the samePRI—that is, during the receive window immediately following thetransmit window of the RF pulse received by the server station 100-S.While not every transmitted RF pulse received by the server station100-S will necessarily pair with an RF pulse received from the serverstation 100-S during the same PRI, those that do then correspond toexchanged timing signals carried over the same MMIT channel.

As mentioned above, and described in more detail below, the respectivearrival times at the server station 100-S and the client station 100-Cof each such pair may be used in TWTT analysis to derive a time offsetbetween the server clock 136-S and client clock 136-C as a timeassociated with the common PRI of the pulse pair. The clock errorcalculator/controller 138 may intermittently output derived time offsetsthat, in turn, may be input to a control algorithm to generate a clockerror/control signal that may be applied to “steer” or correct any timeand/or frequency drift of the client clock 136-C, as indicated. Further,the limited and random availability of MMIT channels for datatransmissions may also result in latency between actual arrival timesand when they are reported and used to derive the corresponding timeoffsets. The clock error calculator/controller 138 may include featuresor functions for compensating not only the sparse and irregular natureof the time-delta measurements, but also for the latency as well. In anexample embodiment, clock error calculator/controller 138 may include orincorporate sequential state estimator, such as a Kalman filter.

The arrows representing the matched filter output to the measurementdata analyzer 140 and the input to the clock error calculator/controller138 are depicted with dotted lines to signify data communications andmeasurement analysis operations. It should be noted that while theclient station 100-C may receive measurement data while operating indata communications mode, the data analysis operations that, forexample, form RF pulse pairs and computes clock error corrections andcontrol, may operate in parallel with RF pulse signal transmissions andreceptions.

In accordance with example embodiments, the server station 100-S and theclient station 100-C may both transmit and receive RF pulses at the sameRF frequency. In an example configuration, each pulse may be centered infrequency at 40 MHz and span 20 MHz. Other frequencies and frequencybandwidths could be used as well. In further accordance with exampleembodiments, both stations may operate in data communications mode usingthe same frequency used for RF pulse transmissions. Such operations maybe carried out using time multiplexing of MMIT channels. An examplearrangement of time multiplexing is described below.

In other example embodiments, timing signals and data communications mayuse different frequencies. This could enable concurrent time and datatransmissions using frequency division multiplexing. Such embodimentsmay also involve additional hardware to support multiple frequencychannels, as well as possibly shared RF power transmission budgetbetween RF frequency channels. While there may be various tradeoffsbetween different embodiments, the general principles of TWTTsynchronization using MMIT channels, as described herein, are largelythe same for all such embodiments, and operations of differentembodiments may be adapted to account for differenttransmission/reception schemes.

In some example embodiments, frequency division multiplexing could beused for client pulse transmissions and server pulse transmissions. Thiscould allow for concurrent pulse transmissions by both the client andserver systems. Again, such embodiments may also involve additionalhardware to support multiple frequency channels, as well as possiblyshared RF power transmission budget between RF frequency channels.

It should be understood that example embodiments using more, fewer,and/or different components and modules than those illustrated by way ofexample in FIG. 1 configured. To the extent that various functions andoperations described could be carried out, at least partly, by softwareinstructions, some of the described components and modules could bemerged, and/or some functions or operations could be implemented indifferent modules than those described. As just one example, the pairingoperation described in connection with the clock error calculatorcontroller 138 could be carried out by a module or component thatcombines the arrival time analyzer 140 and the measurement data analyzer126. As another example, the clock steering operations could be carriedout a clock device that includes software capabilities to implement theclock error calculator controller 138. Other alternative configurationsmay be possible as well.

B. Example Computing Devices and Cloud-Based Computing Environments

FIG. 2 is a simplified block diagram exemplifying a computing device200, illustrating some of the functional components that could beincluded in a computing device arranged to operate in accordance withthe embodiments herein. Example computing device 200 could be a personalcomputer (PC), laptop, server, or some other type of computationalplatform. For purposes of simplicity, this specification may equatecomputing device 200 to a server from time to time, and may also referto some or all of the components of computing device 200 as a“processing unit.” Nonetheless, it should be understood that thedescription of computing device 200 could apply to any component usedfor the purposes described herein.

In this example, computing device 200 includes a processor 202, a datastorage 204, a network interface 206, and an input/output function 208,all of which may be coupled by a system bus 210 or a similar mechanism.Processor 202 can include one or more CPUs, such as one or moregeneral-purpose processors and/or one or more dedicated processors(e.g., application-specific integrated circuits (ASICs), graphicalprocessing units (GPUs), digital signal processors (DSPs), networkprocessors, etc.).

Data storage 204, in turn, may comprise volatile and/or non-volatiledata storage and can be integrated in whole or in part with processor202. Data storage 204 can hold program instructions, executable byprocessor 202, and data that may be manipulated by these instructions tocarry out the various methods, processes, or functions described herein.Alternatively, these methods, processes, or functions can be defined byhardware, firmware, and/or any combination of hardware, firmware andsoftware. By way of example, the data in data storage 204 may containprogram instructions, perhaps stored on a non-transitory,computer-readable medium, executable by processor 202 to carry out anyof the methods, processes, or functions disclosed in this specificationor the accompanying drawings.

Network interface 206 may take the form of a wireline connection, suchas an Ethernet, Token Ring, or T-carrier connection. Network interface206 may also take the form of a wireless connection, such as IEEE 802.11(Wifi), BLUETOOTH®, or a wide-area wireless connection. However, otherforms of physical layer connections and other types of standard orproprietary communication protocols may be used over network interface206. Furthermore, network interface 206 may comprise multiple physicalinterfaces.

Input/output function 208 may facilitate user interaction with examplecomputing device 200. Input/output function 208 may comprise multipletypes of input devices, such as a keyboard, a mouse, a touch screen, andso on. Similarly, input/output function 208 may comprise multiple typesof output devices, such as a screen, monitor, printer, or one or morelight-emitting diodes (LEDs). Additionally or alternatively, examplecomputing device 200 may support remote access from another device, vianetwork interface 206 or via another interface (not shown), such as auniversal serial bus (USB) or high-definition multimedia interface(HDMI) port.

In some embodiments, one or more computing devices may be deployed in anetworked architecture. The exact physical location, connectivity, andconfiguration of the computing devices may be unknown and/or unimportantto client devices. Accordingly, the computing devices may be referred toas “cloud-based” devices that may be housed at various remote locations.

FIG. 3 depicts a cloud-based server cluster 304 in accordance with anexample embodiment. In FIG. 3 , functions of computing device 200 may bedistributed between server devices 306, cluster data storage 308, andcluster routers 310, all of which may be connected by a local clusternetwork 312. The number of server devices, cluster data storages, andcluster routers in server cluster 304 may depend on the computingtask(s) and/or applications assigned to server cluster 304.

For example, server devices 306 can be configured to perform variouscomputing tasks of computing device 200. Thus, computing tasks can bedistributed among one or more of server devices 306. To the extent thatthese computing tasks can be performed in parallel, such a distributionof tasks may reduce the total time to complete these tasks and return aresult.

Cluster data storage 308 may be data storage arrays that include diskarray controllers configured to manage read and write access to groupsof hard disk drives and/or solid-state drives. The disk arraycontrollers, alone or in conjunction with server devices 306, may alsobe configured to manage backup or redundant copies of the data stored incluster data storage 308 to protect against disk drive failures or othertypes of failures that prevent one or more of server devices 306 fromaccessing units of cluster data storage 308.

Cluster routers 310 may include networking equipment configured toprovide internal and external communications for the server clusters.For example, cluster routers 310 may include one or morepacket-switching and/or routing devices configured to provide (i)network communications between server devices 306 and cluster datastorage 308 via cluster network 312, and/or (ii) network communicationsbetween the server cluster 304 and other devices via communication link302 to network 300.

Additionally, the configuration of cluster routers 310 can be based atleast in part on the data communication requirements of server devices306 and cluster data storage 308, the latency and throughput of thelocal cluster network 312, the latency, throughput, and cost ofcommunication link 302, and/or other factors that may contribute to thecost, speed, fault-tolerance, resiliency, efficiency and/or other designgoals of the system architecture.

As noted, server devices 306 may be configured to transmit data to andreceive data from cluster data storage 308. This transmission andretrieval may take the form of SQL queries or other types of databasequeries, and the output of such queries, respectively. Additional text,images, video, and/or audio may be included as well. Furthermore, serverdevices 306 may organize the received data into web page or webapplication representations. Such a representation may take the form ofa markup language, such as the hypertext markup language (HTML), theextensible markup language (XML), or some other standardized orproprietary format. Moreover, server devices 306 may have the capabilityof executing various types of computerized scripting languages, such asbut not limited to Perl, Python, PHP Hypertext Preprocessor (PHP),Active Server Pages (ASP), JAVASCRIPT®, and so on. Computer program codewritten in these languages may facilitate the providing of web pages toclient devices, as well as client device interaction with the web pages.Alternatively or additionally, JAVA® or other languages may be used tofacilitate generation of web pages and/or to provide web applicationfunctionality.

II. Example Operations

FIG. 4 illustrates timing and delay characteristics of an exampleoperational scenario of clock synchronization with the TWTT clocksynchronization system 100, using time signals transmitted over an MMITchannel, in accordance with example embodiments. More particularly, FIG.4 depicts time delays of a signal transmitted from the server station100-S and received by the client station 100-C, and another signaltransmitted by the client station 100-C and received by the serverstation 100-S. Each signal path is shown as being effectively reflectedby a micrometeorite ionization trail, represented by a sloped dashedline, acting as an RF channel. As described above, the ionization trailis made up of free electrons that re-radiate impinging RF radiation viaThompson scattering, such that a portion of impinging RF radiation fromone station is scattered toward the other station. Scattering maytherefore have the effect of reflecting at least a portion of incidentRF radiation, such that the angle of reflection equaling the angle ofincidence.

As indicated, each signal path includes an equipment delay associatedwith transmit processing, a propagation path delay from one station tothe other, and an equipment delay associated with receive processing. Inconsideration of the discussion of FIG. 1 , the equipment delayassociated with transmit processing could correspond to a time between aclock pulse that triggers the digital waveform generator 132 and actualradiation of the amplified RF signal by the antenna 106. Similarly, theequipment delay associated with receive processing could correspond to atime between receiving an RF signal by the antenna 106 and pulsedetection by the matched filter 122. As indicated in FIG. 4 , thetransmit processing delays are τ_(TS) and τ_(TC) at the server andclient stations, respectively; and the receive processing delays areτ_(RS) and τ_(RC) at the server and client stations, respectively. Thepropagation path delay from the antenna of the server station to theantenna of the client station is Δt_(SC); and the propagation path delayfrom the antenna of the client station to the antenna of the serverstation is Δt_(CS).

Assuming an instantaneous time offset δ between the server clock andclient clock, and taking the measured arrival times of received RFpulses at the server station and client station to be T_(arr-S) andT_(arr-C), respectively, it is straightforward to show that the arrivaltimes are related to the time offset by the expressions:

T _(arr-S) =Δt _(CS)+τ_(TC)+τ_(RS)+δ  (1a)

T _(arr-C) =Δt _(SC)+τ_(TS) +T _(RC−δ)  (1b)

These equations may be solved for δ, yielding:

δ=½[T _(arr-S) −T_(arr-C)+(Δt_(SC)−Δt_(CS))+(τ_(TS)−τ_(TC))+(τ_(RC)−τ_(RS))]  (2)

Equation (2) is one general form of a two-way time transfer equation.For application with MMIT channels and identical equipment delays it maybe simplified to an expression involving only the arrival times.

More specifically, for server and client station implementations thatuse the same transmit and receive componentry, it may be reasonablyassumed that the corresponding equipment delays of both stations are thesame. In addition, for both paths scattered by the same MMIT, it may bereasonably assumed that the path delays of both signals are effectivelythe same. With these assumptions, the time offset δ may be expressedsimply as:

δ≈½[T _(arr-S) −T _(arr-C)]  (3)

It may be noted that the assumption that the propagation path delays arenearly equal may appear to neglect possible drift of the physicallocation of an MMIT over the course of the two transmissions, whichcould, in principle, cause the two paths to differ, and thus theirrespective delays to differ. However, from previous studies ofMMIT-based RF communications, it is known that path delays of MMITchannels may change at a rate typically on the order of 10⁻⁷ second persecond. For a time interval between reflections of one millisecond, thedifference in propagation delays of the two paths would be on the orderof 0.1 nanosecond. This may be small enough, therefore, to warrant theassumption that the two propagation path delays are the same, and theirdifference in equation (2) may be neglected.

As described above, in example embodiments the server and clientstations are configured to transmit and receive in periodic PRIs. FIG.5A illustrates the structure of example pulse repetition intervals, inaccordance with example embodiments. Three PRIs are depicted, withleading and trailing ellipses indicating a possibly longer sequence.Each PRI has a transmit window followed by a receive window. In anexample embodiment, PRIs have a period of 25 ms; each transmit window is10 ms and each receive window is 15 ms. These parameters correspond to40 PRIs per second. It should be understood that PRIs could beconfigured with different periods, and transmit and receive windowscould correspondingly be adapted to different PRI periods. Anon-limiting example of a range of possible PRI periods is 10 ms to 250ms. It may be noted that the link budget (power budget on the RF links)could benefit from longer PRI periods, allowing for higher transmissionpower, resulting in longer distance ranges between server and clientstations. However, longer PRI periods could also limit opportunities forusable MMIT channels, since short duration MMITs might be excluded.

At the start of each transmit window, the transceiver may switch totransmit mode and transmit an RF pulse. At the start of each receivewindow, the transceiver may switch to receive mode and carry out receiveoperations described above for detecting an RF if one is received at theantenna. It may be noted that the duration of an actual transmittedpulse may not completely span the transmission window, but will at leastoccur completely within the transmission window. Likewise, the durationof actual receive operations may not completely span the transmitwindow, but will at least occur completely within the transmissionwindow. These operations include ADC sampling and matched filterdetection.

Each PRI may be identified by an index that increments by one for eachsuccessive PRI. The three PRIs shown in FIG. 5 have indices j, j+1, andj+2, as shown. The PRI indices may serve as identifiers of PRIs and maybe used to by the client station to identify transmitted RF pulses withones that are received by the server station. That is, PRI indices inmeasurement data received at the client station from the server station,as described below, may serve as confirmations of transmitted pulsesthat were received by the server station. PRI indices may also be usedto correlate those transmitted RF pulses determined to have beenreceived by the server station with RF pulses received from the serverstation, and thereby form pairs of oppositely-directed pulses thattraversed from one station to the other over the same MMIT channel. Thearrival times of such pairs may then be used in equation (3) todetermine an instantaneous measure of the clock offset δ.

As also described above, measurement data collected and formatted at theserver station may be transmitted to the client station over MMITchannels. In an example embodiment, measurement data may include, foreach RF pulse detected at the server station, an arrival time, a PRIindex, and an SNR measurement characterizing detection strength. Inconsideration of the temporally-random and transient nature of MMITchannels, some degree of economy may be beneficial in determining avolume and format of the measurement data. In an example embodiment,data communications mode may use 8-FSK (frequency shift keying)modulation to transmit measurement data, thereby encoding three bits persymbol.

An example content and formatting of a measurement data message is shownin Table 1. As indicated, 19 bits are allocated to PRI index, 23 bits topulse arrival time, six to SNR, and 16 bits to parity, for a total of 64bits. Two additional bits are added for padding and to round up thetotal to 66, a number divisible by three (the number of bits persymbol). With 19 bits for PRI index, the maximum index divided by 40PRIs per second corresponds to 13,107 seconds. For this configuration,the PRI index rolls over every 13,107 seconds, or every ˜3.6 hours ofcontinuous operation. Any ambiguity that might result from the rollovermay generally be addressed during processing within the 3+ hours betweeneach rollover. For example, the client station could append (or prepend)additional identification to measurement data received in each rolloverperiod. Note that the arrival time may be measured with respect to thestart of the transmit window of the identified PRI; this information maythus be sufficient for the client station to derive clock time ofarrival.

TABLE 1 Data Item Range Resolution Bits PRI index 1-13,107 sec at onePRI 19 40 PRI per sec Pulse Arrival Time 0-2.097 ms 0.25 ns 23 SNR 0-63dB 1 dB  6 Parity N/A N/A 16 Total Bits 64 + 2 padding

FIG. 5B is a conceptual illustration of example transmissions andreceptions between server and client stations of an example clocksynchronization system over micrometeorite ionization trail channels, inaccordance with example embodiments. The two stations are represented byparallel, horizontal timelines, and transmissions are shown as verticalarrows directed from each station's timeline to the other. MMIT channelsare depicted as stippled horizontal bars between the two timelinesoccurring, intermittently in time. During times when an MMIT channel ispresent (e.g., available), transmissions from one station are shown asarriving at (i.e., being received by) the other stations. Conversely,during times when no MMIT channel is present, transmissions from onedon't arrive at the other station. For purposes of illustration, justone second of time is shown, and its full scale is abbreviated byhorizontal ellipse representing present-but-not-illustrated portions ofthe timelines.

As mentioned above, time multiplexing may be used to accommodate bothtiming signal transmissions and measurement data transmissions on asingle RF frequency. In an example time multiplexing scheme, illustratedin FIG. 5B, the first half of each second may be applied to timingsignal transmissions, and the second half to measurement datatransmissions. In the figure, measurement data transmissions are shownas broad arrows directed from the server station to the client station,and labeled “Timing Data.” As with timing signal transmissions,measurement data transmissions make it from the server station to theclient station only during time intervals when MMIT channels occur (areavailable). Other time-multiplexing schemes could be used as well.

As also described above, the relative timing of PRIs at the server andclient stations may be staggered such that the receive windows at eachstation align, at least approximately, with expected arrival times oftransmitted RF pulses from the other station. This relative timing mayfacilitate each given station receiving an RF pulse from the otherstation over the same MMIT channel used to successfully transmit an RFpulse to the other station. Such a pair of pulses, indicated in FIG. 5Bby a dashed rectangle labeled “Pulse Pair,” may be identified at theclient station by first correlating the PRI index in measurement datafrom the server station with the PRI index of a corresponding pulsetransmission from the client station, and then determining if thetransmit window of the corresponding pulse from the client station wasfollowed a receive window that detected a pulse from the server station.

Due to the temporally-random nature of MMIT events and lifetimes, theoccurrence of pulse pairs transmitted and received over the same MMITchannel may be expected to be similarly random. Accordingly, thedurations of the transmit and receive windows may be judiciouslyspecified to optimize the likelihood of forming pulse pairs, in view ofthe general unpredictability of MMIT channel availability. Moreparticularly, existing studies of MMITs and previous experience withMMIT-based RF communications provide information about statisticaldistributions of MMIT events, including event frequencies, locations,and lifetimes. In addition, the inventors have carried out varioussystem trials to help determine optimal values of transmit and receivewindow durations. Thus, the example values above of 10 ms for thetransmit window and 15 ms for the receive window have been determinedbased on existing information as well as new information obtained by theinventors. It should be understood, however, that different values maybe used, and could be updated from time to time-based, for example, onenvironmental or other time-varying factors. Non-limiting examples ofsuch factors could include time of day, time of year, and solaractivity.

The optimal values of transmit and receive window durations may alsoinform aspects of system design connected with the ability to achievevarious transmit and receive operations within applicable timingconstraints. In particular, for the example transmit and receive windowsshown in FIG. 5A, the transmit/receive switch 110 of the server andclient stations 100-S and 100-C needs to be able to switch betweentransmit and receive modes at least as fast as approximately 100 timesper second. Likewise, the power amplifier 108 also needs to be able toswitch this rapidly. Additionally, the potential, relative sparsity ofsuccessful station-to-station timing signal transmissions may furtherinform desired power requirements of the power amplifier 108 forachieving suitable SNR of detected pulses. That is, high SNR detectionsmay help enhance the reliability and statistical confidence inanalytical results. In accordance with example embodiments, then, thepower amplifier 108 may be configured and/or specified for outputting1.5 kW of power. In some example embodiments, this value may be larger,possibly as high as 10 kW of power or more. In view of the specificationof optimal transmit and receive window durations, the power amplifier108 may also need to be able to switch between modes at roughly 100times per second while also operating in an approximate power range of 1kW to 10 kW. To achieve these operational capabilities, the inventorshave customized design, development, and implementation of the poweramplifier 108.

In accordance with example embodiments, the staggering of the PRIsequences at the server and client stations may be achieved by a varietyof bootstrap-like procedures at initial startup of operations. Onenon-limiting example of such a procedure may entail the server stationinitiating operations by transmitting RF pulses according to transmitwindows in its sequence of PRIs. The client station may start its PRIsequence, but initially refrain from transmitting any RF pulses duringits transmit windows, but instead only listen during its receive windowsfor RF pulses from the server station. The client station mayadditionally adjust the timing of its PRI sequence until it beginsreceiving RF pulses from the server station in at least some of itsreceive windows. At this point, the client station may consider that itsPRIs are aligned with an appropriate staggered offset with respect tothe server stations PRIs, and may thus begin transmitting its RF pulsesduring its transmit windows. It should be understood that this examplebootstrapping procedure, or any other that may achieve the requisiterelative alignment of PRI windows may be used.

Since MMIT channels are used for data communications as well as timingsignals (RF pulses), it can happen that the server may accumulate moremeasurement data than can be accommodated over the randomly available,transient MMIT channels. In this sense, the accumulated measurement datamay represent a sort of backlog of data waiting to be transmitted. Inaccordance with example embodiments, the server station may implement aselection algorithm to choose which measurement data to transmit to theclient station. An example algorithm may balance the “age” ofaccumulated data (e.g., how long the data has been waiting to betransmitted) against the quality of the measurement based on SNR. Inmaking the selection, some measurement data may ultimately be discardedinstead of transmitted by the server station. Thus, it can happen thatnot all pulse pairs that actually occurred will ultimately be identifiedby the client server, since not all measurement data used to make pairidentifications will necessarily be transmitted to the client stationfrom the server station.

The effective backlog of measurement data and the selection algorithmused to address it may also result in the client station receivingmeasurement data at times that may be considered “historical” withrespect to the RF pulse (timing signal) transmissions to which themeasurement data apply. Due to the historical nature of the measurementdata received by the client station, as well as the temporally-randomnature of MMIT channels and the possible omission of data measurementsby the selection algorithm, the time offsets derived by the clientstation may tend to be sparse and intermittent (e.g., irregular intime). The historical nature of the measurements may additionallyintroduce latency between the actual arrival times and the times atwhich the time-delta measurements are derived and applied to clockcorrection. In accordance with example embodiments, a controlmodel/algorithm may be applied to the time-delta measurements thatcompensates for its sparse, irregular properties, as well as thelatency, to derive time and frequency corrections that may be applied tothe client clock 136-C in order to synchronize it with the server clock136-S.

This is represented in FIG. 6 , which illustrates example timingprocessing and clock corrections carried out by a client station of anexample clock synchronization system, in accordance with exampleembodiments. FIG. 6 includes just a subset of the elements andcomponents of FIG. 1 related to timing processing and clock correctionscarried out by the client station 100-C. Transmission of measurementdata from the server station 100-S to the client station 100-C isrepresented at the top of the figure by measurement data for PRIindex=J, T_(arr-S)(J) and SNR(J) from the server station to the clientstation. A dashed rectangle below the client station 100-C representsparticular operations, and the components of the client station thatcarry them out.

In an example embodiment, the measurement data analyzer 140 may extractarrival times at the server station of RF pulses and input them to theclock error calculator/controller 138, as indicated. The arrival timeanalyzer 126 may derive arrival times at the client station of pulsesreceived from the server station and input them to the clock errorcalculator/controller 138, as also indicated. Although not explicitlyshown, PRI indices and SNR measurements may also be input to the clockerror calculator/controller 138. The clock error calculator/controller138 may then carry out one or another form the correlations andidentifications, such those described by way of example above, and formpairs of arrival time values corresponding to two oppositely-directed RFpulses that were transmitted between stations over the same MMITchannel. This is represented in FIG. 6 by the indices Ĵ, which representthe subset of J for which pairs have been identified. The arrival timepairs may then be used compute a clock offset for each index Ĵ accordingto equation (3). This is represented in FIG. 6 by the expressionι(Ĵ)=½[T(Ĵ)_(arr-S)−T(Ĵ)_(arr-C)].

As described above, the time offsets for those PRIs which yield them maybe thought of as a stream of intermittent time-delta measurements (i.e.,time offsets). A representative stream is indicated in FIG. 6 as δ₁, δ₂,δ₃, . . . , δ₃₃ along a timeline at corresponding times t₁, t₂, t₃, . .. t₃₃. As also described, the distribution of the time offsets acrossthe timeline is sparse and irregular. In accordance with exampleembodiments, the sparseness and temporal irregularity of the time-deltameasurements may be compensated by a Kalman filter, or more generally, asequential state estimator. The filter may compute a time offset andfrequency drift error which may then be input to a controlalgorithm/model resulting in a frequency correction that may then beapplied to the client clock 136-C to synchronize it with the serverclock 136-S. The process represented graphically in FIG. 6 may becarried out on a continuous, or nearly continuous, basis to maintainsynchronization of the client clock with the server clock. In this way,factors of imperfect oscillator stability that might otherwise cause theclient clock to drift from the server clock may be continuously becompensated and corrected. In some example embodiments, the clock 136-Cmay include, or be part of, a device that integrates softwarecapabilities that could carry out the operations attributed above to theclock error calculator/controller 138.

In practice, while the server station may be largely identical to theclient station, as the reference clock, it may include additionalcomponents or elements that enable it to maintain synchronization withone or another form of time standard, such as GPS. In accordance withexample embodiments, the server station may serve as a reference clockfor multiple client stations, each operating as described by way ofexample above for the client system 100-C.

FIG. 7 illustrates an example RF pulse in frequency space. As shown, thepulse may have a width of 20 MHz with a largely flat power spectraldensity (power distribution), level at approximately 60 dB. It should beunderstood that different power spectral densities could be used for RFpulses, and that different power spectral densities having differentspectral shapes (and power distributions) could be applied with a 20 MHzwidth or a different width. A non-limiting example is a phase-modulatedmaximal-length code sequence. Other waveforms could suppress certainfrequencies to avoid interference with other radio bands, for example.

FIG. 8 illustrates an example of pulse detection in the time domain.Individual data samples are shown as black square with error bars, and asolid line represents a Gaussian fit of the match filter to the sampleddata. The parameters of the fit yield peak power and arrival time.

III. Example Methods

FIG. 9 is a flows chart illustrating a respective example embodiments ofa method 900. The method illustrated in FIG. 9 may be carried out by aclient clock synchronization system (CSS) that includes an antenna, atransceiver coupled with the antenna and configured for switchingbetween transmit and receive modes, and a computing system coupled withthe transceiver and with a client clock. The computing system may beconfigured to carry out, and/or to cause, various operations of theexample method 900. Non-limiting examples of the computing systemcomputing system may include computing device 200 or server cluster 304,for example. However, the method can be carried out by other types ofdevices or device subsystems. For example, the process could be carriedout by a portable computer, such as a laptop or a tablet device. Theclient CSS may be configured for communications with a server CSS overmicrometeorite ionization trail (MMIT) channels. As is known, MMITchannels are distributed randomly in both time and location within theEarth's ionosphere, and have lifetimes distributed randomly in duration.

The embodiments of FIG. 9 may be simplified by the removal of any one ormore of the features shown therein. Further, these embodiments may becombined with features, aspects, and/or implementations of any of theprevious figures or otherwise described herein.

The example 900 may also be embodied as instructions executable by oneor more processors of the one or more server devices of the system orvirtual machine or container. For example, the instructions may take theform of software and/or hardware and/or firmware instructions. In anexample embodiment, the instructions may be stored on a non-transitorycomputer readable medium. When executed by one or more processors of theone or more servers, the instructions may cause the one or more serversto carry out various operations of the example method.

In example embodiments, the computing system of the client CSS may beconfigured to carry out, and/or to cause execution of, variousoperations of the example method 900.

Block 902 of example method 900 may involve, via the antenna, with thetransceiver in transmit mode, transmitting a sequence of radio-frequency(RF) pulses to the server CSS over a first multiplicity of MMITchannels. Transmission information indicating a respective localtransmit identifier and respective transmission time of each transmittedRF pulse may be maintained at the client CSS. For example, thetransmission information could be stored or recorded in a structuredrecord or table.

Block 904 of example method 900 may involve via the antenna, with thetransceiver in receive mode, receiving a first plurality of RF pulsesfrom the server CSS over a second multiplicity of MMIT channels, eachreceived RF pulse consecutively following one of the transmitted RFpulses of the sequence. Reception information indicating a respectivelocal receive identifier and arrival time of each received RF pulse maybe maintained at the client CSS. For example, the reception informationcould be stored or recorded in a structured record or table.

Block 906 of example method 900 may via the antenna, with thetransceiver in receive mode, receiving measurement data from the serverCSS over a third multiplicity of MMIT channels. The measurement data maybe associated with a second plurality of RF pulses received by theserver CSS, and may include, for each of the second plurality, arespective remote receive identifier, a respective arrival time at theserver CSS, and a respective signal-to-noise (SNR) measurement.

Block 908 of example method 900 may involve correlating the measurementdata with the transmission information to identify respectivetransmitted RF pulses of the sequence with respective RF pulses of thesecond plurality received by the server CSS at the respective arrivaltimes with the respective SNR measurements. This operation may thusidentify which of the transmitted RF pulses of sequence were received bythe server CSS.

Block 910 of example method 900 may involve correlating the transmissiontimes of the identified respective transmitted RF pulses with thereception information to determine a third plurality of respectiveRF-pulse pairs. Each respective RF-pulse pair may include (i) aparticular transmitted RF pulse that was received by the server CSS overa particular MMIT channel and (ii) a particular RF pulse that wasreceived from the server CSS over the same particular MMIT channel andconsecutively following transmission of the particular transmitted RFpulse. This operation may thus correspond to the pulse pairs describedabove.

Block 912 of example method 900 may involve applying two-way timetransfer (TWTT) analysis to timing data of each RF-pulse pair to computea set of time offsets of the client clock with respect to a server clockof the server CSS.

Finally, block 914 of example method 900 may involve, applying ananalytical model of clock drift to the set of time offsets tosynchronize the client clock with the server clock.

In accordance with example embodiments, client CSS m a switchedamplifier component coupled with the transceiver, and configured forswitching the transceiver between transmit and receive modes at aswitching rate within a range of [5 Hz, 150 Hz], while operating withina power range of [0.5 kW, 10 kW]. With this arrangement, transmittingwith the transceiver may entail the switched amplifier componentswitching the transceiver to transmit mode, and receiving with thetransceiver may entail the switched amplifier component switching thetransceiver to receive mode.

In accordance with example embodiments, the antenna may be a directionalantenna. With this arrangement, transmitting the sequence of RF pulsesto the server CSS over the first multiplicity of MMIT channels mayinvolve transmitting the sequence of RF pulses at a target azimuthalangle substantially directed to the server CSS, and at a targetelevation angle directed toward the Earth's ionosphere and substantiallycoincident with an incident angle that reflects toward the server CSS.Likewise receiving the first plurality of RF pulses from the server CSSover the second multiplicity of MMIT channels may involve receiving thefirst plurality of RF pulses from the target azimuthal angle, anddirected from the Earth's ionosphere substantially along the targetelevation angle. Here, the terms “substantially directed” and“substantially coincident” signify a general property of directional RFantennas and the radiation pattern they produce. Namely, the radiationpattern may generally have angular distribution in elevation and azimuthsuch that for the power may not be entirely confined to the direction oftransmission. By reciprocity, the radiation pattern also describes theangular distribution of sensitivity to power reception. Thus,transmitting in, or receiving from, a given direction may notnecessarily require an exact or perfect alignment with the givendirection. Hence the term “substantially.”

In accordance with example embodiments, the sequence of RF pulses may betransmitted in a periodic sequence of pulse repetition intervals (PRIs),with one transmitted RF pulse per PRI. Each PRI may include a transmitwindow followed by a receive window. In this configuration, each RFpulse of the sequence may be transmitted during one of the transmitwindows, and each RF pulse of the first plurality may be received duringone of the receive windows. Further, the respective local transmitidentifier of a given transmitted RF pulse of the sequence may be asequence number of the PRI in which the given transmitted RF pulse wastransmitted, and the respective remote receive identifier of a given RFpulse of the second plurality may be a sequence number tracked by theserver CSS of the PRI in which the given RF pulse of the secondplurality was received by the server CSS. With this arrangement,correlating the measurement data with the transmission information mayinvolve matching the respective local transmit identifiers with therespective remote receive identifiers.

In accordance with example embodiments, the PRI may be 25 milliseconds.Other values of PRI period could also be used. A non-limiting example ofa range of possible PRI periods is 10 ms to 250 ms.

In accordance with example embodiments, receiving the first plurality ofRF pulses may involve applying a matched filter to data samples from areceived signal sampled at a fixed sampling rate during each respectivereceive window that consecutively follows each transmitted RF pulse.This may be followed by applying a threshold to the matched filteroutput of each respective receive window to determine which receivewindows yield a detected pulse. In addition, the operations may furtherinclude determining an arrival time of each received RF pulse by fittingan arrival-time curve to each detected pulse.

In accordance with example embodiments, the sampling rate may be 25 MHz.Other sampling rates could be used. A non-limiting example of a range ofsampling rates is 10 Mhz to 100 MHz.

In accordance with example embodiments, fitting the arrival-time curveto each detected pulse may involve applying an interpolation to the datasamples of each detected pulse to compute an effective time resolutionhigher than that of the sampling rate.

In accordance with example embodiments, the set of time offset be orinclude sparse, intermittent time offset measurements with associateduncertainties derived from SNR measurements of both the first pluralityof RF pulses measured by the client CSS and the second plurality of RFpulses measured by the server CSS. Further, the analytical model ofclock drift may include a control algorithm with a state representationof time offset and frequency offset, and a sequential state estimator,such as a Kalman filter, configured to compensate for the sparse,intermittent time offset measurements. The analytical model mayadditionally compensate for latency between actual arrival times andwhen they are reported and used to derive the corresponding timeoffsets. With this arrangement, applying the model of clock drift to theset of time offsets to synchronize the client clock with the serverclock may involve updating a covariance matrix of the analytical modelfor each respective time offset of the set, and then computing anupdated state based on the respective offset; and applying control toadjust the client clock according to the updated state.

In accordance with example embodiments, applying the analytical model ofclock drift to the set of time offsets to synchronize the client clockwith the server clock may involve synchronizing the client clock towithin 4 nanoseconds agreement with the server clock.

In accordance with example embodiments, transmission of RF pulses andreception of RF pulses may be carried out using a common, first RFfrequency, reception of the measurement data may be carried out usingtime multiplexing with a second RF frequency that is the same as thefirst RF frequency, or frequency multiplexing with a second RF frequencythat is different than the first RF frequency.

IV. Conclusion

The present disclosure is not to be limited in terms of the particularembodiments described in this application, which are intended asillustrations of various aspects. Many modifications and variations canbe made without departing from its scope, as will be apparent to thoseskilled in the art. Functionally equivalent methods and apparatuseswithin the scope of the disclosure, in addition to those describedherein, will be apparent to those skilled in the art from the foregoingdescriptions. Such modifications and variations are intended to fallwithin the scope of the appended claims.

The above detailed description describes various features and operationsof the disclosed systems, devices, and methods with reference to theaccompanying figures. The example embodiments described herein and inthe figures are not meant to be limiting. Other embodiments can beutilized, and other changes can be made, without departing from thescope of the subject matter presented herein. It will be readilyunderstood that the aspects of the present disclosure, as generallydescribed herein, and illustrated in the figures, can be arranged,substituted, combined, separated, and designed in a wide variety ofdifferent configurations.

With respect to any or all of the message flow diagrams, scenarios, andflow charts in the figures and as discussed herein, each step, block,and/or communication can represent a processing of information and/or atransmission of information in accordance with example embodiments.Alternative embodiments are included within the scope of these exampleembodiments. In these alternative embodiments, for example, operationsdescribed as steps, blocks, transmissions, communications, requests,responses, and/or messages can be executed out of order from that shownor discussed, including substantially concurrently or in reverse order,depending on the functionality involved. Further, more or fewer blocksand/or operations can be used with any of the message flow diagrams,scenarios, and flow charts discussed herein, and these message flowdiagrams, scenarios, and flow charts can be combined with one another,in part or in whole.

A step or block that represents a processing of information cancorrespond to circuitry that can be configured to perform the specificlogical functions of a herein-described method or technique.Alternatively or additionally, a step or block that represents aprocessing of information can correspond to a module, a segment, or aportion of program code (including related data). The program code caninclude one or more instructions executable by a processor forimplementing specific logical operations or actions in the method ortechnique. The program code and/or related data can be stored on anytype of computer readable medium such as a storage device including RAM,a disk drive, a solid state drive, or another storage medium.

The computer readable medium can also include non-transitory computerreadable media such as computer readable media that store data for shortperiods of time like register memory and processor cache. The computerreadable media can further include non-transitory computer readablemedia that store program code and/or data for longer periods of time.Thus, the computer readable media may include secondary or persistentlong term storage, like ROM, optical or magnetic disks, solid statedrives, compact-disc read only memory (CD-ROM), for example. Thecomputer readable media can also be any other volatile or non-volatilestorage systems. A computer readable medium can be considered a computerreadable storage medium, for example, or a tangible storage device.

Moreover, a step or block that represents one or more informationtransmissions can correspond to information transmissions betweensoftware and/or hardware modules in the same physical device. However,other information transmissions can be between software modules and/orhardware modules in different physical devices.

The particular arrangements shown in the figures should not be viewed aslimiting. It should be understood that other embodiments can includemore or less of each element shown in a given figure. Further, some ofthe illustrated elements can be combined or omitted. Yet further, anexample embodiment can include elements that are not illustrated in thefigures. as

In addition to the illustrations presented in FIGS. 1-8 , furtherillustrative examples and depictions are presented in figures shown inAppendix A and Appendix B that accompany this disclosure.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments will be apparent to those skilled in the art.The various aspects and embodiments disclosed herein are for purpose ofillustration and are not intended to be limiting, with the true scopebeing indicated by the following claims.

What is claimed is:
 1. A client clock synchronization system (CSS)configured for communications with a server CSS over micrometeoriteionization trail (MMIT) channels, the client CSS comprising: an antenna;a transceiver coupled with the antenna and configured for switchingbetween transmit and receive modes; and a computing system coupled withthe transceiver and with a client clock, and configured for carrying outoperations including: via the antenna, with the transceiver in transmitmode, transmitting a sequence of radio-frequency (RF) pulses to theserver CSS over a first multiplicity of MMIT channels, whereintransmission information indicating a respective local transmitidentifier and respective transmission time of each transmitted RF pulseis maintained at the client CSS; via the antenna, with the transceiverin receive mode, receiving a first plurality of RF pulses from theserver CSS over a second multiplicity of MMIT channels, each received RFpulse consecutively following one of the transmitted RF pulses of thesequence, wherein reception information indicating a respective localreceive identifier and arrival time of each received RF pulse ismaintained at the client CSS; via the antenna, with the transceiver inreceive mode, receiving measurement data from the server CSS over athird multiplicity of MMIT channels, wherein the measurement datacomprise, for each of a second plurality of RF pulses received by theserver CSS, a respective remote receive identifier, a respective arrivaltime at the server CSS, and a respective signal-to-noise (SNR)measurement; correlating the measurement data with the transmissioninformation to identify respective transmitted RF pulses of the sequencewith respective RF pulses of the second plurality received by the serverCSS at the respective arrival times with the respective SNRmeasurements; correlating the transmission times of the identifiedrespective transmitted RF pulses with the reception information todetermine a third plurality of respective RF-pulse pairs, wherein eachrespective RF-pulse pair comprises (i) a particular transmitted RF pulsethat was received by the server CSS over a particular MMIT channel and(ii) a particular RF pulse that was received from the server CSS overthe same particular MMIT channel and consecutively followingtransmission of the particular transmitted RF pulse; applying two-waytime transfer (TWTT) analysis to timing data of each RF-pulse pair tocompute a set of time offsets of the client clock with respect to aserver clock of the server CSS; and applying an analytical model ofclock drift to the set of time offsets to synchronize the client clockwith the server clock.
 2. The client CSS of claim 1, further comprisinga switched amplifier component coupled with the transceiver, andconfigured for switching the transceiver between transmit and receivemodes at a switching rate within a range of [5 Hz, 150 Hz], whileoperating within a power range of [0.5 kW, 2.5 kW], wherein transmittingwith the transceiver comprises the switched amplifier componentswitching the transceiver to transmit mode, wherein receiving with thetransceiver comprises the switched amplifier component switching thetransceiver to receive mode.
 3. The client CSS of claim 1, wherein theantenna comprises a directional antenna, wherein transmitting thesequence of RF pulses to the server CSS over the first multiplicity ofMMIT channels comprises transmitting the sequence of RF pulses at atarget azimuthal angle substantially directed to the server CSS, and ata target elevation angle directed toward the Earth's ionosphere andsubstantially coincident with an incident angle that reflects toward theserver CSS, and, and wherein receiving the first plurality of RF pulsesfrom the server CSS over the second multiplicity of MMIT channelscomprises receiving the first plurality of RF pulses from the targetazimuthal angle, and directed from the Earth's ionosphere substantiallyalong the target elevation angle.
 4. The client CSS of claim 1, whereinthe sequence of RF pulses is transmitted in a periodic sequence of pulserepetition intervals (PRIs), one transmitted RF pulse per PRI, whereineach PRI comprises a transmit window followed by a receive window,wherein each RF pulse of the sequence is transmitted during one of thetransmit windows, wherein each RF pulse of the first plurality isreceived during one of the receive windows, wherein the respective localtransmit identifier of a given transmitted RF pulse of the sequence is asequence number of the PRI in which the given transmitted RF pulse wastransmitted, wherein the respective remote receive identifier of a givenRF pulse of the second plurality is a sequence number tracked by theserver CSS of the PRI in which the given RF pulse of the secondplurality was received by the server CSS, and wherein correlating themeasurement data with the transmission information comprises matchingthe respective local transmit identifiers with the respective remotereceive identifiers.
 5. The client CSS of claim 4, wherein the PRI is 25milliseconds.
 6. The client CSS of claim 1, wherein receiving the firstplurality of RF pulses comprises: during each respective receive windowthat consecutively follows each transmitted RF pulse, applying a matchedfilter to data samples from a received signal sampled at a fixedsampling rate; and applying a threshold to the matched filter output ofeach respective receive window to determine which receive windows yielda detected pulse, and wherein the operations further include determiningan arrival time of each received RF pulse by fitting an arrival-timecurve to each detected pulse.
 7. The client CSS of claim 6, wherein thesampling rate is 25 MHz.
 8. The client CSS of claim 6, wherein fittingthe arrival-time curve to each detected pulse comprises applying aninterpolation to the data samples of each detected pulse to compute aneffective time resolution higher than that of the sampling rate.
 9. Theclient CSS of claim 1, wherein the set of time offsets comprises sparse,intermittent time offset measurements with associated uncertaintiesderived from SNR measurements of both the first plurality of RF pulsesmeasured by the client CSS and the second plurality of RF pulsesmeasured by the server CSS, wherein the analytical model of clock driftcomprises a control algorithm with a state representation of time offsetand frequency offset, and a sequential state estimator configured tocompensate for the sparse, intermittent time offset measurements, andwherein applying the model of clock drift to the set of time offsets tosynchronize the client clock with the server clock comprises: updating acovariance matrix of the analytical model for each respective timeoffset of the set; computing an updated state based on the respectiveoffset; and applying control to adjust the client clock according to theupdated state.
 10. The client CSS of claim 1, wherein applying theanalytical model of clock drift to the set of time offsets tosynchronize the client clock with the server clock comprisessynchronizing the client clock to within 4 nanoseconds agreement withthe server clock.
 11. The client CSS of claim 1, wherein transmission ofRF pulses and reception of RF pulses are carried out using a common,first RF frequency, and wherein reception of the measurement data iscarried out using one of: time multiplexing with a second RF frequencythat is the same as the first RF frequency, or frequency multiplexingwith a second RF frequency that is different than the first RFfrequency.
 12. A server clock synchronization system (CSS) configuredfor communications with a client CSS over micrometeorite ionizationtrail (MMIT) channels, wherein MMIT channels are distributed randomly inboth time and location within the Earth's ionosphere, and have lifetimesdistributed randomly in duration, the client CSS comprising: an antenna;a transceiver coupled with the antenna and configured for switchingbetween transmit and receive modes; and a computing system coupled withthe transceiver and with a server clock, and configured for carrying outoperations including: via the antenna, with the transceiver in transmitmode, transmitting a sequence of radio-frequency (RF) pulses to theclient CSS over a first multiplicity of MMIT channels; via the antenna,with the transceiver in receive mode, receiving a first plurality of RFpulses from the client CSS over a second multiplicity of MMIT channels,each consecutively following one of the transmitted RF pulses of thesequence, wherein reception information indicating a respective localreceive identifier and arrival time of each received RF pulse ismaintained at the client CSS; via the antenna, with the transceiver inreceive mode, transmitting measurement data to the client CSS over athird multiplicity of MMIT channels, wherein the measurement datacomprise, for each of a sub-plurality of the first plurality of RFpulses received by the server CSS, a respective local receiveidentifier, the respective arrival time at the server CSS, and arespective signal-to-noise (SNR) measurement.
 13. The server CSS ofclaim 12, wherein the first and second multiplicities of MMIT channelsare at least partially overlapping, and wherein the third multiplicityof MMIT channels is at least partially overlapping with at least one ofthe first or second multiplicities of MMIT channels.
 14. The server CSSof claim 12, wherein the operations further include selecting each givenRF pulse of the sub-plurality from among the first plurality of RFpulses based at least on: the respective SNR of the given RF pulse, oran elapsed time measured from the respective arrival time of the givenRF pulse.
 15. The server CSS of claim 12, further comprising a switchedamplifier component coupled with the transceiver, and configured forswitching the transceiver between transmit and receive modes at aswitching rate within a range of [5 Hz, 150 Hz], while operating withina power range of [0.5 kW, 2.5 kW], wherein transmitting with thetransceiver comprises the switched amplifier component switching thetransceiver to transmit mode, wherein receiving with the transceivercomprises the switched amplifier component switching the transceiver toreceive mode.
 16. The server CSS of claim 12, wherein the antennacomprises a directional antenna, wherein transmitting the sequence of RFpulses to the client CSS over the first multiplicity of MMIT channelscomprises transmitting the sequence of RF pulses at a target azimuthalangle substantially directed to the client CSS, and at a targetelevation angle directed toward the Earth's ionosphere and substantiallycoincident with an incident angle that reflects toward the client CSS,and, and wherein receiving the first plurality of RF pulses from theclient CSS over the second multiplicity of MMIT channels comprisesreceiving the first plurality of RF pulses from the target azimuthalangle, and directed from the Earth's ionosphere substantially along thetarget elevation angle.
 17. The server CSS of claim 12, wherein thesequence of RF pulses is transmitted in a periodic sequence of pulserepetition intervals (PRIs), one transmitted RF pulse per PRI, whereineach PRI comprises a transmit window followed by a receive window,wherein each RF pulse of the sequence is transmitted during one of thetransmit windows, wherein each RF pulse of the first plurality isreceived during one of the receive windows, and wherein the respectivelocal receive identifier of a given RF pulse of the first plurality is asequence number of the PRI in which the given RF pulse of the firstplurality was received.
 18. The server CSS of claim 17, wherein the PRIis 25 milliseconds.
 19. The server CSS of claim 12, wherein receivingthe first plurality of RF pulses comprises: during each respectivereceive window that consecutively follows each transmitted RF pulse,applying a matched filter to data samples from a received signal sampledat a fixed sampling rate; and applying a threshold to the matched filteroutput of each respective receive window to determine which receivewindows yield a detected pulse, and wherein the operations furtherinclude determining an arrival time of each received RF pulse by fittingan arrival-time curve to each detected pulse.
 20. A method of clocksynchronization carried out by a client synchronization system (CSS)configured for communications with a server CSS over micrometeoriteionization trail (MMIT) channels, wherein MMIT channels are distributedrandomly in both time and location within the Earth's ionosphere, andhave lifetimes distributed randomly in duration, the method comprising:via an antenna, with a transceiver in transmit mode, transmitting asequence of radio-frequency (RF) pulses to the server CSS over a firstmultiplicity of MMIT channels, wherein transmission informationindicating a respective local transmit identifier and respectivetransmission time of each transmitted RF pulse is maintained at theclient CSS; via the antenna, with the transceiver in receive mode,receiving a first plurality of RF pulses from the server CSS over asecond multiplicity of MMIT channels, each received RF pulseconsecutively following one of the transmitted RF pulses of thesequence, wherein reception information indicating a respective localreceive identifier and arrival time of each received RF pulse ismaintained at the client CSS; via the antenna, with the transceiver inreceive mode, receiving measurement data from the server CSS over athird multiplicity of MMIT channels, wherein the measurement datacomprise, for each of a second plurality of RF pulses received by theserver CSS, a respective remote receive identifier, a respective arrivaltime at the server CSS, and a respective signal-to-noise (SNR)measurement; correlating the measurement data with the transmissioninformation to identify respective transmitted RF pulses of the sequencewith respective RF pulses of the second plurality received by the serverCSS at the respective arrival times with the respective SNRmeasurements; correlating the transmission times of the identifiedrespective transmitted RF pulses with the reception information todetermine a third plurality of respective RF-pulse pairs, wherein eachrespective RF-pulse pair comprises (i) a particular transmitted RF pulsethat was received by the server CSS over a particular MMIT channel and(ii) a particular RF pulse that was received from the server CSS overthe same particular MMIT channel and consecutively followingtransmission of the particular transmitted RF pulse; applying two-waytime transfer (TWTT) analysis to timing data of each RF-pulse pair tocompute a set of time offsets of the client clock with respect to aserver clock of the server CSS; and applying an analytical model ofclock drift to the set of time offsets to synchronize a client clock ofthe client CSS with a server clock of the server CSS.